Aeolian vibrations represent a threat to the integrity of electrical transmission lines. The fretting fatigue of conductors is thus a major concern. The modelization of the contact conditions at critical points is an important tool in assessing the life of conductors. Treillis points around the last point of contact between the conductor and the pieces of equipment are such critical points. We observe a fully plastic contact condition at these points. Finite element results for the contact between an ellipsoid and a rigid plane and between two wires at different angles are compared with an elastic-plastic microcontact model for elliptical contact areas. These numerical results are then compared with experimental ones for the contact between two wires of a conductor (ACSR Bersfort), showing a very similar relationship between the contact force and the observed contact area. We have a good correlation between the microcontact model and the finite elements ones in the fully plastic contact regime on both the contact area and the contact force for a given interference between bodies. The use of the elastic-plastic microcontact model for elliptical contacts presented in this paper proves to be a strong tool in getting a better understanding of the mechanical behavior at those critical points.